The attached graph represents the graph of the function g(x)
<h3>How to determine the function g(x)?</h3>The function f(x) is an absolute value function.
An absolute value function is represented as:
y = a|x - h| + k
Where
Vertex = (h, k)
From the graph, we have:
(h, k) = (-3, -2)
So, we have:
y = a|x + 3| - 2
Also, we have:
(x, y) = (-1, 0)
So, we have:
0 = a|-1 + 3| - 2
This gives
0 = 2a - 2
Solve for a
a = 1
Substitute a = 1 in y = a|x + 3| - 2
y = |x + 3| - 2
This means that
f(x) = |x + 3| - 2
We have:
g(x) = 2f(x)
This means that:
g(x) = 2(|x + 3| - 2)
So, we have:
g(x) = 2|x + 3| - 4
See attachment for the graph of g(x)
Read more about absolute value functions at:
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